DL之GD：利用LogisticGD算法(梯度下降)依次基于一次函数和二次函数分布的数据集实现二分类预测(超平面可视化)

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DL之GD：利用LogisticGD算法(梯度下降)依次基于一次函数和二次函数分布的数据集实现二分类预测(超平面可视化)
DL之GD：利用LogisticGD算法(梯度下降)依次基于一次函数和二次函数分布的数据集实现二分类预测(超平面可视化)实现

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利用LogisticGD算法(梯度下降)依次基于一次函数和二次函数分布的数据集实现二分类预测(超平面可视化)

设计思路

后期更新……

输出结果

 [ 1.          0.06747879 -0.97085008]
data_x 
 (300, 3) [[ 1.          0.83749402  0.80142971]
 [ 1.         -0.93315714  0.91389867]
 [ 1.         -0.72558136 -0.43234329]
 [ 1.          0.21216637  0.88845027]
 [ 1.          0.70547108 -0.99548153]]
因为Linear_function函数无意义，经过Linear_function函数处理后，data_x等价于data_z
data_y 
 (300,) [-1. -1. -1. -1.  1.]
data_x: (300, 3)
data_z: (300, 3)
data_y: (300,)
[228 106 146 250  91 214  47  49 178  90]
Number of iterations: 26

Plot took 0.10 seconds.
Plot took 0.04 seconds.
Target weights: [ -0.49786797   5.28778784 -11.997255  ]
Target in-sample error: 3.33%
Target out-of-sample error: 6.21%
Hypothesis (N=300) weights: [-0.45931854  3.20434478 -7.70825364]
Hypothesis (N=300) in-sample error: 4.33%
Hypothesis (N=300) out-of-sample error: 6.08%
Hypothesis (N=10) weights: [-1.35583449  3.90067866 -5.99553537]
Hypothesis (N=10) in-sample error: 10.00%
Hypothesis (N=10) out-of-sample error: 12.87%
Error history took 88.89 seconds.
Plot took 17.72 seconds.
Plot took 35.88 seconds.
GD_w_hs[-1] [-1.35583449  3.90067866 -5.99553537]
dimension_z 5
data_x 
 (30, 3) [[ 1.         -0.0609991  -0.15447425]
 [ 1.         -0.13429796 -0.89691689]
 [ 1.          0.12475253  0.36980185]
 [ 1.         -0.0182513   0.74771272]
 [ 1.          0.50585605 -0.04961719]]
因为Linear_function函数无意义，经过Linear_function函数处理后，data_x等价于data_z
data_y 
 (30,) [-1.  1.  1.  1. -1.]

Plot took 1.02 seconds.
Number of iterations: 105

Plot took 1.03 seconds.
Target weights: [-3  2  3  6  9 10]
Hypothesis weights: [-1.23615696 -0.9469097   1.76449666  2.09453304  5.62678124  5.06054409]
Hypothesis in-sample error: 10.00%
Hypothesis out-of-sample error: 15.47%
Plot took 16.58 seconds.
GD_w_hs[-1] [-1.23615696 -0.9469097   1.76449666  2.09453304  5.62678124  5.06054409]

核心代码

def in_sample_error(z, y, logisticGD_function):
    y_h = (logisticGD_function(z) >= 0.5)*2-1
    return np.sum(y != y_h) / float(len(y))


def estimate_out_of_sample_error(Product_x_function, NOrderPoly_Function,Pre_Logistic_function, logisticGD_function, N=10000, Linear_function_h=None):
    x = np.array([Product_x_function() for i in range(N)])
    z = np.apply_along_axis(NOrderPoly_Function, 1, x)
    if not Linear_function_h is None:
        z_h = np.apply_along_axis(Linear_function_h, 1, x)
    else:
        z_h = z
    y = Pre_Logistic_function(z)
    y_h = (logisticGD_function(z_h) >= 0.5)*2-1
    return np.sum(y != y_h) / float(N)


def ErrorCurve_Plot(N,GD_w_hs, cross_entropy_error):
    start_time = time.time()
    fig = plt.figure()   #  figsize=(8, 6)
    ax = fig.add_subplot(1, 1, 1)
    ax.set_xlabel(r'Iteration', fontsize=12)
    ax.set_ylabel(r'In-Sample Error ($E_{in}$)', fontsize=12)
    ax.set_title(r'Gradient Descent Evolution, N={}'.format(N), fontsize=12)
    ax.set_xlim(0, GD_w_hs.shape[0]-1)
    ax.set_ylim(0, 1)
    ax.xaxis.grid(color='gray', linestyle='dashed')
    ax.yaxis.grid(color='gray', linestyle='dashed')
    ax.set_axisbelow(True)
    ax.plot(range(GD_w_hs.shape[0]), np.apply_along_axis(cross_entropy_error, 1, GD_w_hs), 'r-')
    plt.show()
    print('Plot took {:.2f} seconds.'.format(time.time()-start_time))